which two of the following five physical parameters have

Which two of the following five physical parameters have the same dimensions?
(i) Energy density
(ii) Refractive index
(iii) Dielectric constant
(iv) Young’s modulus
(v) Magnetic field

A. (ii) and (iv)

B. (iii) and (v)

C. (i) and (iv)

D. (i) and (v)

Answer : (i) and (iv)

Solution :
$$\eqalign{ & {\text{Energy density = }}\frac{{{\text{Energy}}}}{{{\text{Volume}}}} \Rightarrow u = \frac{E}{V} \cr & {\text{Dimensions of }}u = \frac{{{\text{Dimensions of E}}}}{{{\text{Dimensions of }}V}} \cr & = \frac{{\left[ {M{L^2}{T^{ - 2}}} \right]}}{{\left[ {{L^3}} \right]}} \cr & = \left[ {M{L^{ - 1}}{T^{ - 2}}} \right] \cr} $$
Refractive index is a dimensionless quantity. Dielectric constant is a dimensionless quantity.
$$\eqalign{ & {\text{Young's modulus}}\,{\text{ = }}\frac{{{\text{Longitudinal stress}}}}{{{\text{Longitudinal strain}}}} = \frac{{\frac{F}{A}}}{{\frac{{\Delta l}}{l}}} \cr & = \left[ {M{L^{ - 1}}{T^{ - 2}}} \right] \cr & {\text{Magnetic field = }}\frac{{{\text{Force}}}}{{{\text{Charge}} \times {\text{Velocity}}}} = \frac{F}{{qv}} \cr & = \frac{{\left[ {ML{T^{ - 2}}} \right]}}{{\left[ {AT} \right]\left[ {L{T^{ - 1}}} \right]}} \cr & = \left[ {M{T^{ - 2}}{A^{ - 1}}} \right] \cr} $$

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Basic Physics >> Unit and Measurement

Releted Question 1

The dimension of $$\left( {\frac{1}{2}} \right){\varepsilon _0}{E^2}$$ ($${\varepsilon _0}$$ : permittivity of free space, $$E$$ electric field)

A. $$ML{T^{ - 1}}$$

B. $$M{L^2}{T^{ - 2}}$$

C. $$M{L^{ - 1}}{T^{ - 2}}$$

D. $$M{L^2}{T^{ - 1}}$$

View Answer

Releted Question 2

A quantity $$X$$ is given by $${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}}$$ where $${ \in _0}$$ is the permittivity of the free space, $$L$$ is a length, $$\Delta V$$ is a potential difference and $$\Delta t$$ is a time interval. The dimensional formula for $$X$$ is the same as that of-

A. resistance

B. charge

C. voltage

D. current

View Answer

Releted Question 3

A cube has a side of length $$1.2 \times {10^{ - 2}}m$$ . Calculate its volume.

A. $$1.7 \times {10^{ - 6}}{m^3}$$

B. $$1.73 \times {10^{ - 6}}{m^3}$$

C. $$1.70 \times {10^{ - 6}}{m^3}$$

D. $$1.732 \times {10^{ - 6}}{m^3}$$

View Answer

Releted Question 4

Pressure depends on distance as, $$P = \frac{\alpha }{\beta }exp\left( { - \frac{{\alpha z}}{{k\theta }}} \right),$$ where $$\alpha ,$$ $$\beta $$ are constants, $$z$$ is distance, $$k$$ is Boltzman’s constant and $$\theta $$ is temperature. The dimension of $$\beta $$ are-

A. $${M^0}{L^0}{T^0}$$

B. $${M^{ - 1}}{L^{ - 1}}{T^{ - 1}}$$

C. $${M^0}{L^2}{T^0}$$

D. $${M^{ - 1}}{L^1}{T^2}$$

View Answer

Which two of the following five physical parameters have the same dimensions?
(i) Energy density
(ii) Refractive index
(iii) Dielectric constant
(iv) Young’s modulus
(v) Magnetic field

Releted MCQ Question on
Basic Physics >> Unit and Measurement

The dimension of $$\left( {\frac{1}{2}} \right){\varepsilon _0}{E^2}$$ ($${\varepsilon _0}$$ : permittivity of free space, $$E$$ electric field)

A quantity $$X$$ is given by $${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}}$$ where $${ \in _0}$$ is the permittivity of the free space, $$L$$ is a length, $$\Delta V$$ is a potential difference and $$\Delta t$$ is a time interval. The dimensional formula for $$X$$ is the same as that of-

A cube has a side of length $$1.2 \times {10^{ - 2}}m$$ . Calculate its volume.

Pressure depends on distance as, $$P = \frac{\alpha }{\beta }exp\left( { - \frac{{\alpha z}}{{k\theta }}} \right),$$ where $$\alpha ,$$ $$\beta $$ are constants, $$z$$ is distance, $$k$$ is Boltzman’s constant and $$\theta $$ is temperature. The dimension of $$\beta $$ are-

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Unit and Measurement

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Which two of the following five physical parameters have the same dimensions? (i) Energy density (ii) Refractive index (iii) Dielectric constant (iv) Young’s modulus (v) Magnetic field

Releted MCQ Question on Basic Physics >> Unit and Measurement

The dimension of $$\left( {\frac{1}{2}} \right){\varepsilon _0}{E^2}$$ ($${\varepsilon _0}$$ : permittivity of free space, $$E$$ electric field)

A quantity $$X$$ is given by $${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}}$$ where $${ \in _0}$$ is the permittivity of the free space, $$L$$ is a length, $$\Delta V$$ is a potential difference and $$\Delta t$$ is a time interval. The dimensional formula for $$X$$ is the same as that of-

A cube has a side of length $$1.2 \times {10^{ - 2}}m$$ . Calculate its volume.

Pressure depends on distance as, $$P = \frac{\alpha }{\beta }exp\left( { - \frac{{\alpha z}}{{k\theta }}} \right),$$ where $$\alpha ,$$ $$\beta $$ are constants, $$z$$ is distance, $$k$$ is Boltzman’s constant and $$\theta $$ is temperature. The dimension of $$\beta $$ are-

Practice More Releted MCQ Question on Unit and Measurement

Practice More MCQ Question on Physics Section

Which two of the following five physical parameters have the same dimensions?
(i) Energy density
(ii) Refractive index
(iii) Dielectric constant
(iv) Young’s modulus
(v) Magnetic field

Releted MCQ Question on
Basic Physics >> Unit and Measurement

Practice More Releted MCQ Question on
Unit and Measurement